This is where you need a vintage machine that has the stretch stitch just for polyester. SewJoyce got the only machine I had that would sew it from me so you might want to ask her if you can borrow it.
See if you can find a early 70's sewing machine on CL and buy it just for the quilt. you can find them pretty cheap and the are built really well so it would make a great back up machine!
But it is my understanding that the stretch stitch is the way to go with sewing polyester.
Billy